Questions On Speed Parameters In Space Physics Homework Help

1.You wish to make a round trip from Earth in a spaceship, travelling at constant speed in a straight line for exactly 6 months (as you measure the time interval) and then returning at the same constant speed. You wish further, or your return, to find Earth as it will be exactly 1000 years in the future. (a) To eight significant figures, at what speed parameter β must you travel?
(b) Does it matter whether you travel in a straight line on your journey?

2.The center of our Milky Way galaxy is about 23 000 light year away.
(a) To eight significant figures, at what constant speed parameter would you need to travel exactly 23 000 ly (measured in the Galaxy frame) in exactly 30 y ( measured in your frame)?
(b) Measured in your frame and in light-years, what length of the Galaxy would pass by you during the trip?

3.Your starship passes Earth with a relative speed of 0.9990c. After travelling 10.0 y (your time), you stop at lookout post LP13, turn, and then travel back to Earth with the same relative speed. The trip back takes another 10.0 y (your time). How long does the round trip take according to measurements made on Earth?

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4.Astronomers measure the distance to a particular star to be 6.0 light-years (1 ly = distance light travels in 1 year). A spaceship travels from Earth to the vicinity of this star at steady speed, arriving in 3.50 years as measured by clocks on the spaceship.
(a) How long does the trip take as measured by clocks in Earth’s reference frame?
(b) What distance does the spaceship travel as measured in its own reference frame?

5.In an attempt to reduce the extraordinarily long travel times for voyaging to distant stars, some people have suggested traveling at close to the speed of light. Suppose you wish to visit the red giant star Betelgeuse, which is 430 ly away, and that you want your 20,000 kg rocket to move so fast that you age only 26 years during the round trip.
Part A: How fast (v) must the rocket travel relative to earth?
Part B: How much energy is needed to accelerate the rocket to this speed?
Part C: How many times larger is this energy than the total energy used by the United States in the year 2000, which was roughly 1.0A????11020J?